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Stability of Navier–Stokes discretizations on collocated meshes of high anisotropy and the performance of algebraic multigrid solvers
Author(s) -
Webster R.
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1181
Subject(s) - multigrid method , polygon mesh , interpolation (computer graphics) , instability , anisotropy , reynolds averaged navier–stokes equations , mathematics , reynolds number , algebraic number , computational fluid dynamics , mathematical analysis , geometry , mechanics , physics , classical mechanics , partial differential equation , motion (physics) , quantum mechanics , turbulence
A numerical instability is identified in Navier–Stokes discretizations on meshes of high anisotropy. The instability occurs under conditions of low Reynolds number (and in the Stokes limit) for collocated‐mesh discretizations based on physical (momentum) interpolation schemes. It is responsible for the poor performance reported for some algebraic multigrid solvers (previously attributed to possible deficiencies in the solvers). The problem may be alleviated by not employing uniformly anisotropic meshes. A graded stretching/compaction that leaves part of the domain spanned by elements of moderate aspect ratio can provide sufficient velocity–pressure coupling to stabilize the system. Copyright © 2006 John Wiley & Sons, Ltd.